If I've understood correctly, your house has walls built from insulated lightweight blocks structurally suitable for a domestic dwelling. The wall is a thick single leaf with no cavity. Such blocks need a cladding to waterproof the wall. If I have understood you correctly, the cladding could have been timber/UPVC boards, tiles, or render. Your original builder used thin bricks. This may have been because your local planning department insisted at the planning consent stage that the new houses harmonised in appearance with the rest of the locality. These bricks are not structural, but they form the waterproof cladding, and are similar to thick tiles. The problem seems to be that, unlike tiles, or timber or UPVC boarding, they are linked to the wall with non-corrosion-proof ties rather than fixed directly to the wall. (It's surprising that your builder got away with this, as the building work would have been inspected and approved at the time by your local authority's Building Control department.) Render sticks to a wall, but a long-term consistent bond can be problematic, especially if the render cracks and leaks through, so weakening the bond to the wall proper.
You may have a case against your local authority for allowing a fixing method to be used for the brick cladding which was not corrosion-resistant. One hardly expects properly designed cladding to be detaching itself after only 20 years, but much may depend on how well the brick cladding has been maintained.
If the brick cladding is not structural you don't need the (expensive) services of a structural engineer. As far as I can see, the bricks could be removed and replaced by an alternative cladding. That might be less expensive that trying to stabilize them where they can be seen to be bulging. if the links which connect them to the structural wall are failing in several places, a repair job may not be feasible, and a bodge could lead to problems in the future/if you want to sell the house. You will need at least the advice of a building inspector to determine what is a suitable solution, and how to achieve it so it meets current building regs, is waterproof (which is part of the regs rquirement, obviously), and complements the appearance of the house.
A good builder could probably advise you, but you would need a Building Control completion certificate for the job, for your own peace of mind, and to show to an intending buyer's surveyor and/or conveyancing agent/solicitor. So the job would probably have to be done on a local authority Building Notice.
Alternatively, you might try a private building inspector. These professionals are mainly used by developers for big jobs, but some firms will plan and supervise small jobs like your (you won't consider it to be small, I know!). If you are suitably skilled you could do the work yourself, and the private inspector, who would have to be one approved by your local authority's building control department, would carry out the required inspections, ensure that you were doing the job correctly, gi veyou advice, and issue the completion certificate which would have to be to the local authority standard.
If decide on a complete new cladding job which radically changes the appearance of your house it would be wise to get planning consent before embarking on the job. A lot of such changes go on nowadays without going anywhere near the local planning department. But you can never be sure that a neighbour might not like the appearance of what you were doing, consider it out of keeping with the neighbouring houses etc, and complain to the planning department. Whilst the question might be resolved without your having to change your plans, you never know, so best to be sure that your solution has been approved in advance of your starting work.
